To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right-angled triangle. The frame for the wall with a diagonal brace forms such a triangle, where the height and length of the frame are the perpendicular sides, and the diagonal brace will be the hypotenuse.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
c² = a² + b²
Here:
- The height of the frame is "a", which equals 2.4 m.
- The length of the frame is "b", which equals 4 m.
- The diagonal brace is "c", which we are trying to find.
Substitute the known values into the theorem:
c² = (2.4)² + (4)²
c² = 5.76 + 16
c² = 21.76
Now take the square root of both sides to find the length of the diagonal brace, "c":
c = √21.76
To calculate the square root of 21.76:
c ≈ 4.663 (using a calculator for accuracy)
Now round the result to one decimal place:
c ≈ 4.7 m
Working out: The length of the diagonal brace to the nearest tenth is 4.7 meters.
Answer: 4.7 m
